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Optica Applicata, Vol. XL, No. 4, 2010

An application of swarm intelligence binary particle swarm optimization (BPSO) algorithm to multi-focus image fusion

XINMAN ZHANG, LUBING SUN*, JIUQIANG HAN, GANG CHEN

MOE Key Lab for Intelligent Networks and Network Security, School of Electronics and Information Engineering, Xi’an Jiaotong University, Xi’an, 710049, China*Corresponding author: [email protected]

In this paper, an optimal and intelligent multi-focus image fusion algorithm is presented, expectedto achieve perfect reconstruction or optimal fusion of multi-focus images with high speed.A synergistic combination of segmentation techniques and binary particle swarm optimization(BPSO) intelligent search strategies is employed in salience analysis of contrast feature-visionsystem. Also, several evaluations concerning image definition are exploited and used to evaluatethe performance of the method proposed. Experiments are performed on a large number of imagesand the results show that the BPSO algorithm is much faster than the traditional genetic algorithm.The method proposed is also compared with some classical or new fusion methods, such as discretewavelet-based transform (DWT), nonsubsampled contourlet transform (NSCT), NSCT-PCNN(pulse coupled neural networks (PCNN) method in NSCT domain) and curvelet transform.The simulation results with high accuracy and high speed prove the superiority and effectivenessof the present method.

Keywords: multi-focus image fusion, binary particle swarm optimization (BPSO), perfect reconstruction,swarm intelligence, image definition evaluation.

1. IntroductionDue to the limited depth-of-focus of optical lenses in CCD devices (e.g., camerawith finite depth of field, light optical microscope, etc.), it is often impossible to getan image that contains all relevant objects in focus. In an image captured by thosedevices, only the objects within the depth of field are focused, while other objects areblurred. A possible way to solve this problem is image fusion, in which one canacquire a series of pictures with different focus settings and fuse them to producean image with extended depth of field. The fused image will then hopefully containall the relevant objects in focus. Images of this kind are useful in many fields, such asdigital imaging, microscopic imaging, remote sensing, computer vision and robotics[1, 2].

Multiscale transforms are very useful for analyzing the information content ofimages for fusion purposes. Various methods based on the multiscale transforms have

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been proposed, such as Laplacian pyramid-based, gradient pyramid-based, ratio-of--low-pass pyramid-based, discrete wavelet-based (DWT). The basic idea is to performa multi-resolution decomposition on each source image, then integrate all thesedecompositions to form a composite representation, and finally reconstruct the fusedimage by performing an inverse multi-resolution transform [3].

More recently, many novel image fusion algorithms have emerged rapidly andperformed satisfactorily, which include so called beyond-wavelets [4], for example,curvelet transform (CT), and nonsubsampled contourlet transform (NSCT). The CT issuitable for analyzing image edges such as curve and line characteristics. The maindifference between NSCT and other beyond-wavelets algorithms is that the contourlettransform can efficiently capture the intrinsic geometrical structures in natural imagessuch as smooth contour edges and is a fully shift-invariant, multiscale andmultidirection expansion [4, 5]. Pulse coupled neural networks (PCNN) is a novelbiological neural network based on the experimental observations of synchronouspulse bursts in cat and monkey visual cortex. It is characterized by the global couplingand pulse synchronization of neurons. These characteristics benefit image fusionwhich makes use of local image information [6]. PCNN has been successfully used inimage fusion. However, all these methods have some errors when comparing the fusedmulti-focus image with the reference image.

These techniques belong to any of the following categories: pixel-based, window--based or region-based. Pixel-based methods concentrate on a single pixel andwindow-based methods concentrate on a k×k window, where k is very small. It isknown that even a very small error in registration results in mismatch of all the pixelsunder consideration. Pixel-based methods would not be able to tackle the situationand produce erroneous results. So, they are sensitive to misregistration or noise.Window-based and region-based techniques are better in this respect but they requirea sequence of complex and time-consuming processes and hence take a largecomputation time [7].

ZHANG et al. [8] proposed a genetic search strategies based image fusion algorithm(GA algorithm). This method can accomplish absolute restoration or optimizedfusion of multi-focus images to the reference image. Here absolute restoration is calledzero-error reconstruction or perfect reconstruction. Compared to other algorithms,GA algorithm demonstrates superior fusion results. However, the operation speed ofthe algorithm is not very satisfactory. In this paper, we propose an improved andintelligent algorithm, in which we choose the binary particle swarm optimization(BPSO) method to speed up the algorithm. A large number of image experiments verifythe rapidity and superior performance of the algorithm proposed.

The paper is organized as follows: Section 2 presents a detailed BPSO fusionalgorithm and a schematic diagram, followed by the measures we suggested, whichspecially describe the definition of multi-focus images in the next section.Experimental results and analysis are given in Sections 4 and 5. In the last section,the paper is concluded.

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2. Multi-focus image fusion scheme-based on BPSO search

The goal in multi-focus image fusion is to capture and preserve in a single outputimage all the “clear” part that is present within two input images. The basic fusionalgorithm will be described in Section 2.1. In this section, the algorithm firstdecomposes the source images into blocks. Fusion then proceeds by selecting a clearerblock according to uniform parameter. Section 2.2 shows the detailed process andprocedure of the proposed BPSO fusion algorithm. This section solves the problem ofchoosing block size that optimizes the fused image furthest and accelerating the blocksearching process.

2.1. The basic algorithm [8]

Considering the contrast vision feature in human vision system, we address uniformparameter to test the definition of focus images. Uniform parameter is moreoptimal than block variance, which represents the deviations between block pixeland block mean. We shall treat an image as a two-dimensional array of pixels, andthe pixel in the i-th row and the j-th column shall be denoted by I (i, j ). Using thisnotation, we define dk , namely the uniform parameter of partition block of an image Ias follows:

(1)

where μ k is the mean of block Bk , and m×n is the block size. In the following, we shall assume that there are two out-of-focus inputs A and B.

The fusion algorithm breaks up both of them into smaller square regions, i.e., m×nblocks. Denote the i-th image block pair by BAi and BBi. Then image fusion isperformed based on uniform parameter of each block. The i-th block BFi of the fusedimage is then constructed as

(2)

where dAi and dBi are uniform parameters of the relative blocks BAi and BBi of twoinput images A and B, respectively. Given two of these blocks (one from each sourceimage), the contrast vision model is to determine which one is clearer.

Next, each partition block is incorporated according to Eqs. (1) and (2), so the clearregions are selected and this process yields a merged image F. If the same objectappears more legible (in other words, with better contrast), in image A than B, afterfusion the object in image A will be preserved while the object in image B will beignored.

dk1

m n×--------------------

I i j,( ) μk–

μk------------------------------------

i j,( ) Bk∈∑=

BFiBAi, d Ai d Bi>

BBi, otherwise⎩⎨⎧

=

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2.2. BPSO search fusion algorithm

Image fusion is carried out as the key step, that is, the most important, to searchthe desired fused image in terms of different block sizes. Fusion then proceeds byselecting the clearer block in constructing the final image. Even though it seemstheoretically reasonable that a very small block size will lead to the best global optimalsolution, it is practically infeasible due to a large amount of computation and lowspeeds.

Here, we propose BPSO search strategies in the image block searching process andhave a good effect.

Particle swarm optimization (PSO) is a population based algorithm, which isinspired by the social behavior of animals such as fish schooling and bird flocking.This evolutionary computation technique, based on the information about the previousbest performance of each particle and the best previous performance of its neighbors,has been largely applied as a problem-solving technique in engineering and computerscience. In PSO, each particle can communicate with every other individual, forminga fully connected social network. In this case, each particle is attracted toward the bestparticle (best problem solution) found by any member of the entire swarm. BPSOalgorithm is a binary version of particle swarm optimization algorithm, which issuitable to solve discrete optimization problems. In this algorithm, the position ofeach particle is encoded in the binary format. The velocity of a particle is defined as“the rate of change of position”, that is, each bit of velocity represents the probabilityof changing the corresponding bit of position from its previous state to itscomplementary value. Thus, every particle moves in a binary space to search the bestproblem solution [9, 10].

If we consider two sources A and B as the input images to be fused, the fusionoptimization problem that we examine here can be considered as a search problem.The optimized image is obtained by combining different image blocks chosenaccording to adaptive BPSO search algorithm.

In detail, the BPSO strategies consist of the following steps:1. Determine the proper population number P and initialize the position of each

particle by stochastic method. Experiments indicated that, within a certain range,when P increases, the fusion effects are better, while the operation speed becomesslower. The most optimized block size is likely to be the position number. Supposethat for an M×N image, the search range is (1, M – 1) and (1, N – 1) for simplicity, sothe position of particle Ci is composed of two parts representing blocks’ length andwidth code

where u refers to the position row code length (of size log 2 M ), v refers to the positioncolumn code length (of size log 2 N ) and i belongs to a range of [1, P ] [11].

Ci ni u v+, ni u v 1–+, … ni u 2+, ni u 1+, mi u, mi u 1–, … mi 2, mi 1,=


2. Compute the fitness function of each particle. Here we mean the spatialfrequency, i.e., spatial frequency (SF). With a larger SF value, the correspondingparticle position is more advantageous and it is more possible to search its surroundingareas.

3. Record the best previous position of each particle and the best previousposition of the global population according to the fitness function. Intuitively, we canthink of the function as some measure of profit, utility, or goodness that we want tomaximize.

4. Use BPSO strategies to update each particle position. In BPSO, each particleis indicated by a binary bit string. Its position updating progress is shown in Fig. 1.The difference between the present position of a particle and its previous bestposition, and the difference between the present position of a particle and the bestposition of all particles are expressed by two bit strings, respectively, called differencevectors [12]. Both difference vectors have P bits. Each bit indicates whetherthe corresponding elements of the two position vectors are the same or not. If they arethe same, the bit value is 0, otherwise 1. This comparison process is similar tothe logical operation XOR. Then randomly generate two vectors c1 and c2, and performAND operation with the two random vectors, respectively. The two random binary bitvectors are equivalent to the random numbers in real-valued PSO algorithm, the effectof which is to increase the capacity of exploration and exploitation of the algorithm.Then, performing OR operation between the two temporary bit strings generated fromthe previous step, we get the velocity vector of the algorithm. Finally, the new position

Fig. 1. The position updating progress of a particle.

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vector is obtained after XOR operation between the velocity vector and the initialposition vector.

5. Perform genetic folding operation. If the terminate condition is satisfied, endthe operation, if not, go to the next step. Here, the terminate condition is met whenthe ratio of the average fitness value of the present population to the average fitnessvalue of the parent population locates in the interval [1, α ]. The choice of α shouldensure good convergence speed of the algorithm and avoid premature. In image visionapplications, the optimal value of α is 1.005. The folding operation times are not morethan log 2 (M N/4).

6. Choose the optimized blocks to reach the best effect.Figure 2 illustrates the block diagram of the proposed multi-focus image fusion

scheme.

The detailed procedure of BPSO search fusion algorithm is described as follows: 1. Begin2. Input the source images3. Initialize the population and the parameters, e.g., P, α and the greatest folding

operation times4. Check whether each position is properly coded5. While (the folding operation times are within bounds)6. Begin7. Compute the fitness function of each particle, respectively8. Record the global best position and the individual best position9. Judge whether the terminate condition is satisfied, if satisfied, exit the loop

10. Use BPSO strategies to update the position of each particle 11. Check whether each position is properly coded12. End13. Choose the optimized block and perform fusion14. Output the fused image 15. End

Fig. 2. Block diagram of the proposed multi-focus image fusion scheme.


3. Performance measures The performance measures used in this paper provide some quantitative comparisonamong different fusion schemes, mainly aiming at measuring the definition ofan image. Consider R as the reference image and F the fused image, both of size M×N.F(i, j ) is the gray value of pixel at the position (i, j ).

3.1. Root mean square error (RMSE)RMSE is the most valuable performance evaluation criterion when reference image isavailable. It is defined as

(3)

If RMSE equals 0, it corresponds to the perfect image reconstruction. Namely,the fused image is a perfect image, which has been achieved through accuratereconstruction of multi-focus images to the reference image.

3.2. Spatial frequency (SF)

Spatial frequency indicates the overall active level of an image. At the same time itrepresents minus details of contrast and texture commutation characteristic. The spatialfrequency for a fused image is defined as follows:

(4)

where RF and CF are the row frequency and column frequency, respectively:

(5)

(6)

3.3. Visual sensitivity (VS)The visual sensitivity of an image, which originated from the human visual system, isdefined as

(7)

where μ is the intensity mean value of the image.

RMSE

R i j,( ) F i j,( )–2

j 1=

N

∑i 1=

M

∑M N×

--------------------------------------------------------------------------=

SF RF2 CF2+=

RF 1M N×

-------------------- F i j,( ) F i j 1–,( )–2

j 2=

N

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M

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CF 1M N×

-------------------- F i j,( ) F i 1– j,( )–2

i 2=

M

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N

∑=

VS 1M N×

-------------------- F i j,( ) μ–μ

-----------------------------------j∑

i∑=

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3.4. Energy of Laplacian (EOL) of the image [13]Another focus measure for analyzing high spatial frequencies associated with imageborder sharpness is the Laplacian operator

(8)

where

The fusion results with smaller value of RMSE or larger values of EOL, SF, andVS are generally considered better.

4. Experimental results

Experiments are performed on several sets of images to evaluate the proposed fusionalgorithm. The results on two sets of fully registered 256-level gray images will beshown here (size of 128×128). For comparison purposes, the fusion is alsoperformed using the DWT method [14], the CT method [4], the NSCT method [4],the NSCT-PCNN method (PCNN method in NSCT domain) [6] and the previouslyproposed algorithm – GA method [8]. Experiments are implemented on an Intel Core22.61 GHZ computer with 2.00 GB RAM. The simulation software is Matlab 7.01.

The parameters of our BPSO algorithm are: the population number P = 8, α == 1.005, the greatest folding times are 12. The parameters of GA algorithm are:the population number P = 10, α = 1.005, the crossover ratio Pc = 0.8, the mutationratio Pm = 0.1, the greatest folding times are 12. For the DWT method, the waveletbasis “db8” and a decomposition level of 3 are used. The curvelet transform isimplemented into two levels, and the second level contains eight orientations.The fusion rule is the maximum-selection scheme and the verification rule is majorvoting in 5×5 window. Three decomposition levels, with 2, 4, 16 directions fromcoarser scale to finer scale, are used in NSCT algorithm, in which the lowpass subbandcoefficients and the bandpass subband coefficients are simply merged by the averagingmethod and the maximum regional gradient method, respectively. In NSCT-PCNNmethod, parameters of PCNN are set as follows: αL = 0.06931, αθ = 0.2, β = 0.2,VL = 1.0, Vθ = 20, and the maximal iterative number is 200. For NSCT parts, four scalesof decomposition with 1, 2, 4, 16 directions are used, and the PCNN and SF-PCNNrules are used in the low-frequency and high-frequency domain, respectively.

For the two sets of fully registered images, we consider two blurring cases in detail.In one case, two objects areas are not overlapped blurred, just like Fig. 3. Figure 4shows another case that two objects areas are overlapped blurred. Fusion results ofthe two blurring cases by using five algorithms are shown in Figs. 3 and 4, respectively.It is hard to subjectively find the difference between the fusion results among the five

EOL fii fj j+( )2

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algorithms. So, we use RMSE to evaluate the overall performance of the differentalgorithms, and use EOL, SF, and VS to evaluate the definition of the fused images.

Tables 1 and 3 show the fusion results of DWT, CT, NSCT and NSCT-PCNNmethods. Considering the randomness of GA and BPSO method, 100 repeated runsare performed, and the average results are summarized in Tabs. 2 and 4.

From Tab. 1 through Tab. 4, we can see that both BPSO method and GA methodcan accomplish absolute restoration or optimized fusion according to RMSE. The fusedimages of DWT, CT, NSCT and NSCT-PCNN methods all have some small errors.According to EOL, SF, and VS, the fusion effects (definition) of BPSO and GA methodare almost the same, but the execution speed of BPSO method is much faster. In

T a b l e 1. Objective fusion performance of DWT, CT, NSCT and NSCT-PCNN algorithm onprocessing Fig. 3.

T a b l e 2. Objective fusion performance of GA and BPSO algorithm on processing Fig. 3.

T a b l e 3. Objective fusion performance of DWT, CT, NSCT and NSCT-PCNN algorithm onprocessing Fig. 4.

T a b l e 4. Objective fusion performance of GA and BPSO algorithm on processing Fig. 4.

Evaluation parametersAlgorithm RMSE EOL SF VS Time [s]DWT 1.9005 8.9050 22.2230 0.4188 0.0610CT 1.4748 8.8581 22.0738 0.4176 0.5470NSCT 1.4038 8.9796 22.1066 0.4170 55.953NSCT-PCNN 1.0313 8.6956 21.9918 0.4188 46.281

Evaluation parameters (Avg: average results of 100 repeated runs)Algorithm Min(RMSE) Avg(RMSE) Avg(EOL) Avg(SF) Avg(VS) Avg(time) [s]GA 0 0.1582 8.7469 22.0741 0.4195 0.1891BPSO 0 0.1523 8.7464 22.0740 0.4195 0.1175

Evaluation parametersAlgorithm RMSE EOL SF VS Time [s]DWT 1.3934 2.0413 33.8861 0.8153 0.0780CT 0.8123 2.0547 33.9101 0.8140 0.6400NSCT 0.8913 2.0603 33.8947 0.8149 56.047NSCT-PCNN 0.7800 2.0454 33.8618 0.8157 45.641

Evaluation parameters (Avg: average results of 100 repeated runs)Algorithm Min(RMSE) Avg(RMSE) Avg(EOL) Avg(SF) Avg(VS) Avg(time) [s]GA 0.5462 0.6233 2.0515 33.9095 0.8163 0.2133BPSO 0.5462 0.5879 2.0521 33.9143 0.8164 0.1327


Table 2, the average run time of GA is 0.1891 s, while BPSO is 0.1175 s, decreasingby 37.9%. And in Tab. 4, the average run time of GA is 0.2133 s, while BPSO is0.1327 s, decreasing by 37.8%. Compared with the other three methods, BPSO is onlyslower than the DWT method. So, the conclusion can be drawn that the proposedalgorithm has higher accuracy and high speed.

5. Digital camera multi-focus image applicationIn practice, images are usually captured by a hand-held or mobile camera. Due tothe limited depth-of-field of digital cameras, it is often not possible to get an imagethat contains all relevant objects sharply focused. And the multi-focus digital cameraimages are usually not registered. So, it is an important issue to study image fusion ofdigital camera images.

Experiments are performed on the “Lab” images (size of 480×640), which are notregistered, as shown in Fig. 5. Figures 5a and 5b are the source images focused onthe clock and the student, respectively. Figure 5c is the image obtained using

Fig. 5. Digital camera image fusion. Source image (focus on the clock, size of 480×640) – a; source image(focus on the student) – b; auto-focus image – c; fused image obtained by DWT algorithm – d; fusedimage obtained by CT algorithm – e; fused image obtained by NSCT algorithm – f ; fused image obtainedby NSCT-PCNN algorithm – g ; fused image obtained by GA algorithm – h; fused image obtained byBPSO algorithm – i.

a b c

d e f

g h i

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the auto-focus function of the camera. Fusion results on using DWT, CT, NSCT,NSCT-PCNN, GA and the proposed BPSO method are shown in Figs. 5d–5h.Objective comparisons of their performance are given in Tab. 5. For a clearcomparison, parts of the source images and fusion results are extracted and put intoFig. 6 [15], and the difference images between the fused image and the source imagesare given in Fig. 7.

T a b l e 5. Objective fusion performance of the five algorithms on processing Fig. 5.

Evaluation parametersAlgorithm EOL SF VS Time [s]DWT 3.6313 12.9274 0.3119 1.2340CT 3.5523 12.9463 0.3158 10.359NSCT 3.6884 12.8550 0.3161 1071.4NSCT-PCNN 3.5135 12.9235 0.3121 844.12GA 3.4385 12.9107 0.3241 5.8900BPSO 3.4774 12.9475 0.3222 1.5940

Fig. 6. Parts of the fused results of Figs. 5a–5i, respectively.

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As illustrated in Fig. 6, we can see that the BPSO method and the GA methodperform better. There are more or less some blurred parts in the results of the otherthree methods. Notice that there is a slight movement of the student’s headbetween Figs. 6a and 6b, and this influences the clarity. GA and BPSO method solvethe problem and get the legible images. Figure 7 shows the difference images betweenthe fused image and the source images. For the focused regions, the difference betweenthe source image and the fused image should be zero [3]. For example, in Fig. 5athe clock is clear, and in Fig. 7a the difference between Fig. 5d and Fig. 5a in the clock

Fig. 8. The 12 test images.


region is blank. This demonstrates that the whole focused area is contained in the fusedimage successfully. In this way, from Fig. 7, we can conclude that the BPSO and GAmethod can extract more legible information from source images.

From Table 5, we can see that the run time of GA method is 5.8900 s, while forthe BPSO method it is 1.6570 s, decreasing by 71.9%. The BPSO method is muchfaster than the GA method, only slightly slower than the DWT method. According tothe other three evaluation measures, the fused image definition of BPSO method isalso satisfactory.

In addition to the above images, extensive reference or digital camera images(including color images) are employed in our tests and have verified the high speedand high accuracy of BPSO algorithm. Figure 8 lists some of them.

6. Conclusions

A multi-focus image fusion algorithm combing human visual feature and BPSOintelligent search strategies is presented in this paper. Several image definitionmeasures are used to objectively evaluate the performance of the approach proposed.Compared with the previously proposed approach – GA algorithm, the BPSOmethod can also realize absolute restoration or optimized fusion of multi-focus imageto the reference image, and its running speed is faster. We have also compared ouralgorithm with the DWT method, the curvelet transform (CT) method, the NSCTmethod and the NSCT-PCNN method. Experiments on 20–30 sets of manuallyproduced multi-focus images and digital camera images show that the proposedmethod is an adaptive and reliable image fusion technique with high speed and highaccuracy, and it is robust to misregistration and noise. So, the proposed BPSO imagefusion method is statistically significant.

Acknowledgements – The work is supported by the grants from the National Natural Science Foundationof China (No. 60972146 and No. 60602025).

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Received January 30, 2010in revised form April 19, 2010

an application of swarm inte lligence binary particle ... · of the present method. keywords:...

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